answer:Separate the whole numbers from the fractional parts: = {20} + {dfrac{7}{8}} - {3} - {dfrac{5}{8}} Bring the whole numbers together and the fractions together: = {20} - {3} + {dfrac{7}{8}} - {dfrac{5}{8}} Subtract the whole numbers: = 17 + {dfrac{7}{8}} - {dfrac{5}{8}} Subtract the fractions: = 17 + dfrac{2}{8} Combine the whole and fractional parts into a mixed number: = 17dfrac{2}{8} Simplify to lowest terms: = 17dfrac{1}{4}

answer:To maximize revenue, we need to find the values of {eq}q {/eq} and {eq}p {/eq} that maximize the revenue function {eq}R(q) = qp(q) {/eq}. {eq}begin{align*} displaystyle R(q) & =qp(q) & =q(500qe^{-00016q^{2}}) & =500q^2e^{-16q^{2}} end{align*} {/eq} Solving the equation {eq}R'(q) =0 {/eq} for {eq}q {/eq}: {eq}begin{align*} displaystyle R'(q)& =0 frac{mathrm{d}}{mathrm{d}q}(500q^2e^{-16q^{2}})& =0 100qe^{-16q^2}-16000q^3e^{-16q^2}& =0 -2e^{-16q^2}q(4q-1)(4q+1)& = 0 q & = 0,frac{1}{4}, - frac{1}{4} end{align*} {/eq} The solution {eq}q=displaystyle - frac{1}{4} {/eq} is extraneous while the values of {eq}R(q) {/eq} at {eq}q=0 {/eq} and {eq}q= displaystyle frac{1}{4} {/eq} are {eq}0 {/eq} and {eq}11.5 {/eq}, respectively, so {eq}R(q) {/eq} is maximized if {eq}q= displaystyle frac{1}{4} {/eq}. We also solve for {eq}p {/eq} when {eq}q= displaystyle frac{1}{4} {/eq}: {eq}begin{align*} displaystyle p(q) & =500qe^{-16q^{2}} pleft(frac{1}{4}right) & =500left(frac{1}{4}right)e^{-16left(frac{1}{4}right)^{2}} pleft(frac{1}{4}right) & =45.98 end{align*} {/eq} Hence, {eq}p = 45.98 {/eq} dollars and {eq}q= displaystyle frac{1}{4} {/eq} servers sold per month maximize revenue.

answer:European exploration significantly impacted North America in several ways. One of the most devastating effects was the introduction of new diseases to the native population. Native Americans, who had no immunity against diseases like smallpox, influenza, measles, and chickenpox, suffered massive casualties as a result of these epidemics. Additionally, the arrival of Europeans brought about cultural exchanges, trade, and the spread of religion. However, the explorers' technological superiority, particularly their use of advanced weapons such as single-shot muskets, enabled them to gain a military advantage over native tribes, leading to conflicts and territorial changes. The establishment of European colonies also contributed to the displacement and subjugation of indigenous peoples, as well as the transatlantic slave trade, which had long-lasting social and economic implications.

answer:We can construct the bijection as follows: For any function h: X rightarrow B, define a new function h': Y rightarrow B by h'(y) = h(f^{-1}(y)). This gives a mapping h mapsto h'. In other words, we compose the function h with the inverse of the bijection f to obtain a function that maps from Y to B. This mapping is a bijection, as it is both injective and surjective.